The United States and Japan will step up their defence cooperation to deal with the threat from nuclear-armed North Korea as tensions in East Asia remain high, officials from the two allies said on Thursday.

Commonwealth argues Day was ineligible

Lawyers for the commonwealth have argued former Family First senator Bob Day was ineligible to serve in parliament alleging he received an indirect pecuniary interest through a lease agreement.

Stephen Donaghue QC, representing Attorney-General George Brandis, made the case during a High Court hearing in Canberra on Tuesday.

The court, sitting as the Court of Disputed Returns, will determine whether Mr Day had a direct or indirect pecuniary interest in a lease agreement between the owner of his electorate office premises and the federal government.

Under the constitution, such an arrangement would disqualify him from sitting in parliament.

Mr Day, who started his first term in the Senate on July 1 2014, didn't wish to move into the electorate office of his South Australian predecessor Don Farrell, favouring a space in an office building he previously owned.

The senator's company and family trust sold 77 Fullarton Road, Kent Town in Adelaide to Fullarton Investments under an arrangement which B & B Day loaned $2.1 million, the court was told.

There was an understanding Fullarton Investments would receive rent from the commonwealth and make vendor finance payments to the Day trust.